Engineering Fundamentals: An Introduction to Engineering
Engineering Fundamentals: An Introduction to Engineering
6th Edition
ISBN: 9780357391273
Author: Saeed Moaveni
Publisher: Cengage Learning US
Question
Book Icon
Chapter 20, Problem 17P
To determine

Find the equivalent annual worth of the cash flow diagram.

Expert Solution & Answer
Check Mark

Answer to Problem 17P

The equivalent annual worth of the cash flow diagram is $3868.37.

Explanation of Solution

Given data:

The normal interest rate (i) is 8%.

Formula used:

Formula to calculate the annual worth for the given cash flow diagram is,

AW=[$5000(PA,i,n)(AP,i,n)$2000(PA,i,n)(PF,i,n)(AP,i,n)+$8000(PF,i,n)(AP,i,n)+$5000(AF,i,n)] (1)

Here,

F is the future cost,

P is the present cost,

A is the uniform series payment,

i is the normal interest rate, and

n is the number of years.

Refer the Problem 20.17 Figure in the textbook, the equation (1) is rewritten with respect to the given number of years is,

AW=[$5000(PA,i,6)(AP,i,10)$2000(PA,i,3)(PF,i,4)(AP,i,10)+$8000(PF,i,8)(AP,i,10)+$5000(AF,i,10)] (2)

Formula to calculate the present cost for the given uniform series payment is,

(PA,i,n)=[(1+i)n1i(1+i)n] (3)

Formula to calculate the uniform series payment for the given present cost is,

(AP,i,n)=[i(1+i)n(1+i)n1] (4)

Formula to calculate the present cost for the given future cost is,

(PF,i,n)=[1(1+i)n] (5)

Formula to calculate the uniform series payment for the given future cost is,

(AF,i,n)=[i(1+i)n1] (6)

Calculation:

To calculate the equivalent annual worth of the cash flow diagram:

Substitute 8% for i, and 6 for n in equation (3) to find (PA,i,6).

(PA,i,6)=[(1+(8%))61(8%)(1+(8%))6]=[(1+0.08)610.08(1+0.08)6]=4.623

Substitute 8% for i, and 10 for n in equation (4) to find (AP,i,10).

(AP,i,10)=[(8%)(1+(8%))10(1+(8%))101]=[0.08(1+0.08)10(1+0.08)101]=0.149

Substitute 8% for i, and 3 for n in equation (3) to find (PA,i,3).

(PA,i,3)=[(1+(8%))31(8%)(1+(8%))3]

(PA,i,3)=[(1+0.08)310.08(1+0.08)3]=2.577

Substitute 8% for i, and 4 for n in equation (5) to find (PF,i,4).

(PF,i,4)=[1(1+(8%))4]=[1(1+0.08)4]=0.735

Substitute 8% for i, and 8 for n in equation (5) to find (PF,i,8).

(PF,i,8)=[1(1+(8%))8]=[1(1+0.08)8]=0.540

Substitute 8% for i, and 10 for n in equation (6) to find (AF,i,10).

(AF,i,10)=[(8%)(1+(8%))101]=[0.08(1+0.08)101]=0.069

Substitute 4.623 for (PA,i,6), 0.149 for (AP,i,10), 2.577 for (PA,i,3), 0.735 for (PF,i,4), 0.540 for (PF,i,8), and 0.069 for (AF,i,10) in equation (2) to find AW.

AW=[$5000(4.623)(0.149)$2000(2.577)(0.735)(0.149)+$8000(0.540)(0.149)+$5000(0.069)]=$3868.37

Therefore, the equivalent annual worth of the cash flow diagram is $3868.37.

Conclusion:

Thus, the equivalent annual worth of the cash flow diagram is $3868.37.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
For the loading system acting on the beam shown in Fig.(1) Determine the reactions at the supports. 2kN/m Fig. (1) 4kN/m
The 4-story building shown below has a dead load D = 90 psf, floor live load, L = 110 psf. The roof and floors have the same D and L loads. The length of columns is 24 ft at the ground level and 12 ft for all other floors. The column ends are pins (Kx = Ky = 1.0) and Lx = Ly for all columns. (Use LFRD Method where applicable).1) Determine Pu on interior columns B2-4, B2-1, and side column C1-1  2) Use Table 4-1a (p. 4-12 to 4-24) in AISC to select the lightest W shapes for these columns 3) Use Table 4-4 (p. 4-68 to 4-83) in AISC to select lightest square HSS shape for the columns
The 4-story building shown below has a dead load D = 90 psf, floor live load, L = 110 psf. The roof and floors have the same D and L loads. The length of columns is 24 ft at the ground level and 12 ft for all other floors. The column ends are pins (Kx = Ky = 1.0) and Lx = Ly for all columns. Determine Pu on interior columns B2-4, B2-1, and side column C1-1  (Use LFRD where applicable).
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Engineering Fundamentals: An Introduction to Engi...
Civil Engineering
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Cengage Learning
Text book image
Fundamentals Of Construction Estimating
Civil Engineering
ISBN:9781337399395
Author:Pratt, David J.
Publisher:Cengage,
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning